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 Class 8 Chapter 4, ( Algebraic Formulas and Equations )

 

Algebraic Formulas and Equations
Category	Formula
Basic Identity	(x + y)^2 = x^2 + 2xy + y^2
	(x - y)^2 = x^2 - 2xy + y^2
	(x + y)(x - y) = x^2 - y^2
	(x + a)(x + b) = x^2 + (a+b)x + ab
Cubic Identity	(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3
	(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3
	x^3 + y^3 = (x+y)(x^2 - xy + y^2)
	x^3 - y^3 = (x-y)(x^2 + xy + y^2)
Quadratic Equation	x = (-b ± √(b^2 - 4ac)) / 2a
Exponent Law	a^m × a^n = a^(m+n)
	a^m / a^n = a^(m-n)
	(a^m)^n = a^(mn)
	a^0 = 1 (a ≠ 0)
Logarithm Law	log_a(mn) = log_a m + log_a n
	log_a(m/n) = log_a m - log_a n
	log_a(m^n) = n log_a m